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If ! denote the area of any triangle wit...

If `!` denote the area of any triangle with semi-perimeter , then

A

`!lt(s^(2))/2`

B

`!gt(s^(2))/4`

C

`!lt(s^(2))/4`

D

`!lts^(2)`

Text Solution

Verified by Experts

Let a, b, c be the lengths of the sides of the triangle.
Now,
A.M.gt G.M.
`rArr(s+s-a+s-b+s-c)/4gtabs(s(s-a)(s-b)(s-c))^(1//4)`
`rArrs/2gtDelta^(2//4)rArr(s^(2))/4gtDeltarArrDeltalt(s^(2))/4`
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Knowledge Check

  • The ratio of sides of a triangle is 3:4:5 and area of the triangle is 72 square unit. Then the area of an equilateral triangle whose perimeter is same as that of the previous triangle is

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